This issue of is the second volume of the proceedings of theCLE/AIPS Event – Science, Truth and Consistency1, held at the University of Campinas (Unicamp), in Campinas, State of São Paulo, Brazil, during August 23–28, 2009, under the joint sponsorship of the Centre for Logic, Epistemology and the History of Science (CLE) of Unicamp and of the International Academy of Philosophy of Science (AIPS), based in Brussels. The meeting was meant as a tribute to the eightieth anniversary of Prof. Dr. Newton Carneiro Affonso da Costa, the pioneer Brazilian researcher in the areas of logic and philosophy of science2.
The International Academy of Philosophy Science (AIPS) was officially founded on January 22, 1949 in Brussels, with the aim of promoting the intellectual cooperation of scientists and philosophers of different backgrounds, concerned with the synthesis of science, philosophy and theology, especially at a time when a demand for specialization was pressing universities worldwide. Among its foun-der members were not only scientists concerned with such synthesis, such as Bernays, Beth, Born, Bridge, Carnap, Church, Curry, Des-touches, Frank, Gonseth, Heisenberg, Kleene, Kotarbinski, Pauli, Piaget, Poly, Popper, Sierpinski, Schrödinger, Whittaker, Wiener, Yukawa, but scientists creators of innovative new theories such as Einstein (relativity), Bohr (quantum mechanics), de Broglie (wave mechanics), Brower (intuitionism) and Fréchet (abstract sets and sym-metric spaces). Since its creation, the Academy organized 50 regular meetings in various European countries, in the United States, Mexico
1The first volume was published as a special issue ofStudia Logica(2011), v. 97,
entitledThe Legacy of Newton da Costa, with a fragment of the contributions to the
CLE/AIPS Event.
2Organizing Committee: I.M. Loffredo D’Ottaviano (Chair) for CLE; D.
and Peru. The meeting of which this volume is part of the procee-dings was the first one in Brazil. Evandro Agazzi is the AIPS pre-sident.
The Centre for Logic, Epistemology and the History of Science (CLE) at Unicamp, aiming at bringing together scientists from the various branches of scientific and philosophical knowledge, has pro-moted since its official establishment on April 7, 1977, more than a hundred medium and large size events. This CLE/AIPS meeting had the participation of scholars in the fields of philosophy, logic, epistemology, history and philosophy of science, their contributions being focused on issues related to da Costa’s work, with emphasis on interdisciplinarity.
Newton Carneiro Affonso da Costa has known how to crystal-lize, in a series of logical calculations, the power of contradictory reasoning in science and philosophy.
Since his youth da Costa has been interested in issues of logic and the foundations of mathematics. Very motivated by his mother, Silvia Carneiro Affonso da Costa, and his aunt, Carmen Carneiro, with the support of one of his uncles, Milton Carneiro, then Pro-fessor of History of Philosophy at the Federal University of Paraná (UFPr), he started reading philosophy through French translations of the dialogues of Plato and texts of Aristotle.
In the years 1950 da Costa began to develop his ideas about the importance of the study of contradictory theories. In 1958, inNotas sobre o conceito de contradição (Notes on the concept of contradiction), published by the Anais da Sociedade Paranaense de Matemática (An-nals of the Mathematics Society of Paraná), da Costa proposed the fol-lowing Principle of Tolerance in Mathematics: From the syntactic and semantical point of view, every theory is permitted, provided that it is not trivial.
show mathematically that contradictions can be profitably kept in theories and rational contexts that express knowledge. Moreover, his calculi were the first to bestow the formal tools needed for proces-sing the contradictions that the new science, together with the old philosophy, were looking for. Half a century later, not only the phi-losophical debate but also information theory, linguistics, quantum physics and psychoanalysis make use of this intellectual tool.
Having presented his ideas at the meeting of the Brazilian Society for the Advancement of Science (SBPC) held in Curitiba in July 1962, da Costa published his first notes about inconsistent but non-trivial calculi in the journal Ciência e Cultura (Science and Culture) in the same year.
Beginning with his Thesis Sistemas Formais Inconsistentes (Incon-sistent Formal Systems) da Costa initiates, in 1963, the publication of a series of papers in theComptes Rendus de l’Académie de Sciences de Paris, in which he introduces his well known hierarchies of para-consistent calculi. In Sistemas Formais Inconsistentes, the objectives of his pioneer work are clearly defined. He introduces his hierar-chies of logical calculi for the study of inconsistent (contradictory) but non-trivial theories: the hierarchy of propositional calculi Cn, 1 ≤ n ≤ ω, the hierarchy of predicate calculiC∗
n, 1 ≤ n ≤ ω, the hierarchy ofpredicate calculi with equalityC=
n, 1 ≤ n≤ ω, and the hierarchy of calculi of descriptions Dn, 1 ≤ n ≤ ω . The new lo-gics are devised to be maximally conservative over classical logic, in particular, Modus Ponens must still hold, and whenever the prin-ciple of non-contradiction(¬(A&¬A))holds for a formulaA, then A must behave like a classical formula. A paraconsistent logic aims at accommodating possibly inconsistent pieces of information in a formal framework where useful deductions can be made.
Since 1964, da Costa’s logics and paraconsistent logic in general have been attracting increasing interest.
concer-ning the semantics and decidability of those calculi and a general theory of valuations, algebraic structures associated to such systems, paraconsistent set theories, logics of higher order, model theory, pa-raconsistent differential calculi and some recent applications to infor-matics, computer science, engineering, medicine and technology.
Several applications of paraconsistent logics have been developed, such as theories based on semantically closed languages, ethics, doxas-tic, deontic and epistemic logics, theory of probability, foundations of quantum mechanics, artificial intelligence, cognitive sciences, foun-dations of the infinitesimal calculus, founfoun-dations of science and its philosophical analysis.
One of the relevant concepts, formally and rigorously introdu-ced by da Costa, is the pragmatic notion ofquasi-truth, a notion that generalizes Tarski’s correspondence definition of truth. Quasi-truth can be formulated by means of a wide generalization of standard model theory and is related to what da Costa calls “abstract Galois theory”. For him the concept of quasi-truth is a reasonable truth concept inherent to the empirical sciences, in particular to physical theories. It can be shown that the logic of quasi-truth is paracon-sistent and is reduced to classical logic when quasi-truth is identified with truth.
Da Costa taught at the Federal University of Paraná (UFPr), Uni-versity of São Paulo (USP) and UniUni-versity of Campinas (Unicamp), being nowadays invited Collaborator Professor at the Federal Uni-versity of Santa Catarina (UFSC), Brazil. Open and sensitive to new opportunities, Newton da Costa had an important role in crea-ting the Centre for Logic, Epistemology and the History of Science (CLE) at Unicamp in 1976, and has remained up to date as one of CLE’s most important and active members.
Asso-ciation of Symbolic Logic, of whose council he was a member during 1970-1973 and whose Committee on Logic in Latin-America he chai-red during 1970-1976.
In 1982 he was the founding editor of the first international jour-nal in the area of non-classical logics,The Journal of Non-Classical Lo-gic, that was merged in 1991 with theJournal of Applied Non-Classical Logics, edited by Hermès/Lavoisier France.
His personal archives, donated to the Historical Archives on the History of Science of CLE, have been research subject for several students and researchers.
A man of political convictions, he never ceased to share ideas with his students, and had his share of difficulties during the rigid authoritarian period, in the last 60’s and 70’s, in Brazil.
Among the awards he has received during his career let us men-tion:Moinho Santista Prize, 1993;Jabuti Prize in Exact Sciences, 1995; Ordem do Pinheiro Medal of the State of Paraná Government, for scientific merit, 1996;Scientific Medal of Merit “Nicolaus Copernicus”, awarded by the University of Torun, Poland, 1998; Scientific Merit of the Federal University of Paraná/Association of Former Students, 1998;Emeritus Citizen of the State of Paraná, for scientific merit. Da Costa is also a member of many academies, including: Honorary Member of theInstitute of Philosophy of Peru, 1975; Honorary Mem-ber of the Research Institute of Philosophy of the University of Lima, 1980; Corresponding Member of the Academy of Sciences of Chile, 1982; Member of the Academy of Sciences of the State of São Paulo, Brazil, 1978; Member of the International Institute of Philosophy in Paris, 1989; and Honorary Member of AIPS.
Verlag published the first encyclopaedic book on paraconsistency, Paraconsistent logic: essays on the inconsistent, by Routley, Priest and Norman; in 2000, volume 125, n. 12, of Synthèsewas dedicated to Newton da Costa.
Since 1990, the item “paraconsistent logic” appears in the AMS Subject Classification. The series of meetings “World Congress on Paraconsistency” began in 1994 in Ghent, Belgium, followed by the second edition in Juquehy, São Paulo, Brazil, in 2000, dedicated to da Costa’s 70th anniversary; the third and fourth editions were held in 2003 (Toulouse, France) and 2008 (Melbourne, Australia), respec-tively.
The intense dedication of Professor da Costa has never been li-mited to scientific work. He has been also dedicated to the guidance of several students in Master Dissertations and Doctoral Theses, hel-ping to form the first generation of Brazilian logicians. Among them are: Ayda Ignez Arruda (his first student and collaborator), Antonio Mário Sette, Elias Humberto Alves, Lafayette de Moraes, Luiz Paulo de Alcântara, Andrea M. Altino Loparic, Walter Carnielli, Tarcísio Pequeno, Décio Krause, Edélcio de Souza, Juliano Maranhão and Itala M. Loffredo D’Ottaviano.
“But the position I adopt is in constant change, trying to adapt itself to the evolution of science and knowledge in general. It is, as Hermann Weyl would say, an attempt to climb the heavens. Perhaps this is the only admissible attitude, rationally spea-king, of a philosopher or a scientist”. (da Costa, Unicamp Pro-fessor Emeritus Ceremony)
As of today, Newton da Costa has published around 250 papers, books, articles and notes. More than 3000 citations of his books and papers, in more than 10 languages are known. He has been visiting scholar in research institutions in the Americas, Europe and Austra-lasia.
The magnitude and impact of da Costa’s work made him one of the most cited Brazilian scientists. Specialized meetings have been devoted, in part or in whole, to discuss and debate his work in Brazil, Belgium, Poland, United States, Canada, Denmark and Italy.
In a personal correspondence with da Costa, von Wright deemed paraconsistent logic as the best creation in logic during the second half of the 20th century, having changed the paradigms of logic.
The creative and innovative work of da Costa and his unquestio-nable academic leadership were crucial to the emergence of an inter-nationally recognized “Brazilian School of Logic”.
We, the guest editors of this volume, are proud of being among his collaborators and friends.
TheCLE/AIPS Eventwas attended by over one hundred mem-bers of the international philosophical scientific community, featu-ring CLE and AIPS members and former da Costa’s students and collaborators.
During the opening ceremony, hosted by the Rector of Unicamp, Prof. Dr. Fernando Ferreira Costa, the President of AIPS, Prof. Dr. Evandro Agazzi, announced that Newton da Costa had been elected anHonorary Memberof the International Academy of Philosophy of Science, being the first Brazilian to receive so great honour.
on the subject Consistency, Truth and Ontology. During the event Prof. da Costa was awarded with the title of “Professor Emeritus of the University of Campinas”. This deliberation of the University Board was a fair homage to this intellectual and teacher who, with his example of work, dedication and ethical behaviour, has so much contributed to the development and academic quality of Unicamp and has so much ennobled the Brazilian Philosophy and Science. Ac-cording to da Costa’s words, during the Unicamp Professor Emeritus Ceremony:
“Since I was 15 years old, I have nurtured a great interest for knowledge, with emphasis on scientific knowledge, which I have tried, step by step, to understand and unveil. This in-cluded not only formal disciplines (such as logic and mathema-tics), but also natural sciences, especially physics, and human sciences. It became immediately clear to me that, with such an aim, I should become acquainted with the formal sciences, for they constitute, as it were, the pillars of other sciences. It is clear that such an aim needs to go hand in hand with a phi-losophical quest. Although it is possible to analyze science and its presuppositions without invoking a philosophical stance, the resulting analysis is incomplete and somewhat superficial. And those who lack familiarity with science, in turn, cannot develop properly a philosophy of science. Thus, I became se-riously involved with both philosophy and science Currently, a non-trivial philosophy of science can only grow via interdisci-plinary studies, with the cooperation of specialists of different fields. I was then led, I repeat, to study and investigate various fields of knowledge, an activity that has been conducted by more than half a century”.
de Apoio ao Ensino, à Pesquisa e à Extensão (FAEPEX, Unicamp, Brazil), the State of São Paulo Research Foundation (FAPESP, Bra-zil), the National Council for Scientific and Technological Develop-ment (CNPq, Brazil) and Coordenação de AperfeiçoaDevelop-mento de Pes-soal de Nível Superior (CAPES, Brazil). We are also grateful to Uni-camp for its support, and especially to the staff of CLE for their enthusiastic contribution to the success of this unique event.
This special issue ofManuscritocontains the papers of the mem-bers of AIPS and part of the submitted papers to the proceedings of theCLE/AIPS Event -Science, Truth and Consistency. A third book of proceedings is forthcoming, as a special issue ofPrincipia Interna-tional Journal of Epistemology.
The three guest editors acknowledge the technical support of Fá-bio Maia Bertato, researcher of CLE, and Teófilo Reis, who adequa-ted the papers to the editorial norms ofManuscrito.
We are also grateful to the referees, whose competent advice was of decisive help in shaping this volume.
EVANDRO AGAZZI ITALA M. L. D’OTTAVIANO DANIELE MUNDICI
Department of Philosophy Centre for Logic, Epistemology and Department of Mathematics University of Genoa, Italy the History of Science University of Florence Department of Humanities Department of Philosophy Italy Univ. Autónoma Metropolitana - Cuajimalpa University of Campinas mundici@math.unifi.it
Mexico Brazil
